Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20261176 | C2 | semidirect |
| 3. C2×#15690753 | C2 | semidirect |
| 4. #20260547 | C2 | semidirect |
| 5. #20260541 | C2 | semidirect |
| 6. #20260519 | C2 | semidirect |
| 7. #473×C97 | C2 | semidirect |
| 18. #15690750 | C22 | semidirect |
| 19. C2×#13095486 | C22 | semidirect |
| 21. C2×Q16×C97 | C22 | semidirect |
| 23. #108×C97 | C22 | semidirect |
| 92. C97 | #2194 | semidirect |
| 96. #473 | D97 | semidirect |
| 106. C2×Q16 | C2×D97 | semidirect |
| 115. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261540 | 2 |
| #20261176 | 2 |
| C2×#15690753 | 2 |
| #20260547 | 2 |
| #20260541 | 2 |
| #20260519 | 2 |
| #473×C97 | 2 |
| #2194 | 97 |